26 (number)

In mathematics

• 26 is the seventh discrete semiprime (2 \times 13) and the fifth with 2 as the lowest non-unitary factor thus of the form (2.q), where q is a higher prime.
• 26 is the smallest even number n such that both n + 1 and n − 1 are composite.
• With an aliquot sum of 16, within an aliquot sequence of five composite numbers (26,16,15,9,4,3,1,0) to the Prime in the 3-aliquot tree.
• 26 is the only integer that is one greater than a square (5 + 1) and one less than a cube (3 − 1).
• 26 is a telephone number, specifically, the number of ways of connecting 5 points with pairwise connections.
• There are 26 sporadic groups.
• The 26-dimensional Lorentzian unimodular lattice II25,1 plays a significant role in sphere packing problems and the classification of finite simple groups. In particular, the Leech lattice is obtained in a simple way as a subquotient.
• 26 is the number of permutations of {a, b, c, d, e} with only one ascent.
• There are 26 faces of a rhombicuboctahedron.
• The gyroelongated square cupola (J23), elongated square gyrobicupola (J37), gyroelongated triangular bicupola (J44), and snub square antiprism (J85) each have 26 faces.{{cite journal|last=Johnson|first=Norman|authorlink=Norman Johnson (mathematician)|title=Convex Solids with Regular Faces|journal=Canadian Journal of Mathematics|volume=18|year=1966|pages=169–200|doi=10.4153/CJM-1966-021-8
• When a 3 × 3 × 3 cube is made of 27 unit cubes (e.g. Rubik's Cube), 26 of them are viewable as the exterior layer.
• A cube has 26 elements: 6 faces, 12 edges, and 8 vertices.
• A 26-sided polygon is called an icosihexagon.
• φ(26) = 12 = φ(σ(26)).

Properties of its positional representation in certain radixes

Twenty-six is a repdigit in bases three (2223) and twelve (2212).

In base ten, 26 is the smallest positive integer that is not a palindrome to have a square (262 = 676) that is a palindrome.

In religion

• 26 is the gematric number, being the sum of the Hebrew characters () being the name of the god of Israel – YHWH (Yahweh).
• 26 is also the gematric number for GOD with the corresponding substitutions in English (i.e. A=1, B=2, C=3, and so on)
• In the Tenrikyo religion of Japan, 26 is frequently used, since it marks the lunar calendar date of its founder Nakayama Miki's first divine revelation and also her death.

In science

• Iron is the 26th element in the periodic table.
• Messier 26 is an open cluster of stars in the southern constellation of Scutum.
• NGC 26 is a spiral galaxy in the Pegasus constellation.
• The maximum time difference between two timezones is 26 hours.

In other fields

• 26 is the number of the letters in the Latin Alphabet.

References

References

1. {{Cite OEIS
2. "The number 26, between 25 and 27".
3. "Sloane's A000085 : Involution numbers". OEIS Foundation.
4. Wilson, Robert. (2009-12-14). "The Finite Simple Groups". Springer Science & Business Media.
5. {{Cite OEIS. A000295. Eulerian numbers.
6. Saiber, Arielle. "Measured Words: Computation and Writing in Renaissance Italy". University of Toronto Press.
7. "polygon".
8. {{cite OEIS. A006872